Emotions

Emergent MOTif in IntercONnected Systems

The project

The spontaneous formation of regular spatial patterns in complex systems is an outstanding feature of many systems found in Nature. This project aims to contribute to understanding the emergence of such motifs in complex or random systems whose microscopic rules are described by simple rules yet resulting in rich mathematical models. A key aspect of our proposal is characterizing the emerging motifs’ geometric shapes and their fluctuations. We intend to tackle these themes by combining our expertise in the fields of statistical mechanics, integrability, complex networks and dynamical systems, reinforcing thus the burgeoning collaboration between the UNamur Institute for complex systems (naXys) and the UCLouvain Institute for Research in Mathematics and Physics (IRMP) and setting it into a solid and durable ground. By using analytical and numerical methods, we intend to pursue three research axes.

The artic curve phenomenon

The first research axis addresses the so-called arctic curve phenomenon in random tiling and vertex models of planar statistical mechanics. The phenomenon refers to the emergence of deterministic patterns known as arctic curves in a particular scaling limit of these models. The curves spatially separate the models’ solid, liquid, or even gaseous phases. Finding and characterizing these arctic curves, in particular by exploiting integrability properties, is an active research field with yet a great deal of open problems. We intend to contribute to it by investigating so-called surface-on-surface models or higher-spin vertex models, for which characterizations of the arctic phenomenon remain to be found, benefiting from both the analytical expertise of the UCLouvain team and the numerical know-how of the UNamur team.

The universality of fluctuations in the vicinity of arctic curves

The second research axis focuses on the universality of the fluctuations in the vicinity of arctic curves. Universality refers to the appearance of identical features in totally unrelated problems or models. A paradigmatic example is the characterization of the fluctuations around arctic curves in some tiling models by the celebrated Tracy-Widom distribution, which governs the (unrelated) statistics of the largest eigenvalue of certain random matrices. Such observations hint at deep properties of the fluctuations in arctic phenomena, which we intend to investigate.

Random walks in complex networks

The third research axis concerns patterns and universality related to random walks in complex networks. A focus will be the study of the so-called loop-erased random walks resulting from a chronological loop erasure applied to simple random walks. Loop-erased random walks have been thoroughly investigated in regular structures and are connected to a host of models of statistical mechanics, such as spanning trees or the Abelian sandpiles, and continuum theories, for example the Schramm-Loewner evolutions. Combining our knowledge and previous work in these fields with the UNamur team’s expertise in complex network theory, we plan to address the generalizations of loop-erased random walks to complex networks and several simultaneous random walkers.

The research team

PI (spokesperson)

Co-PI

Co-PI
     

Prof. Timoteo CARLETTI

University of Namur (UNamur)

Namur Institute for Complex Systems, naXys

Prof. Christian HAGENDORF

Université catholique de Louvain (UCLouvain)

Institut de recherche en mathématique et physique, IRMP

Prof. Philippe RUELLE

Université catholique de Louvain (UCLouvain)

Institut de recherche en mathématique et physique, IRMP

About the team

Timoteo CARLETTI

Timoteo Carletti is Full Professor at the Department of mathematics and at the Namur Institute for Complex Systems, naXys, at UNamur. After obtained a master in physics at the university of Florence (Italy), he received his PhD in mathematics at the University of Florence (Italy) and at “Institut de Mécanique Céleste et de calcul des Ephémérides” (IMCCE) in Paris (France). After several postdoctoral research stays - including Paris XI (Paris, France), IMPA (Rio de Janeiro, Brazil), "Scuola Normale Superiore" (Pisa, Italy) - in 2005 he moved to Belgium where he was hired at the University of Namur as lecturer, then as Professor (2008), and finally as Full Professor (2011) in the Department of applied Mathematics. In 2010 he was among the creators of the Namur Center for Complex Systems (naXys) of which he assumed the leadership from 2010 to 2014.

His current research interests lie in the study of dynamical systems defined on top of complex networks. He is interested in studying conditions for the emergence of synchronization in systems interacting via networks or higher-order networks. He also obtained several results concerning the onset of Turing patterns for reaction-diffusion systems defined on networks or higher-order networks.

Christian HAGENDORF

Christian Walmsley Hagendorf is a Professor at the Institute of Research for Mathematics and Physics (IRMP) at UCLouvain. He studied physics at the Martin-Luther-Universität Halle Wittenberg (Germany), the Université Pierre and Marie Curie Paris 6, and the École Normale Supérieure Paris (France). After receiving his PhD degree from Université Pierre and Marie Curie Paris 6 in 2009, he has held postdoctoral positions at the University of Virginia (United States) and the Université de Genève (Switzerland), and then joined IRMP in 2013. His current research focuses on exactly solvable models in low-dimensional statistical mechanics, such as the six- and eight-vertex models, quantum integrable spin chains and their relations with enumerative combinatorics.

Philippe RUELLE

Former research interests : modular invariance in conformal field theory, formulation of quantum mechanics on p-adic fields, W-algebras and Hamiltonian reductions of WZWN theories.
Current research interests : critical lattice statistical models (sandpile models, dimer model, spanning trees, combinatorics of tiling problems, arctic phenomena, random walks, discrete fermions) and their description by conformal field theories (in particular logarithmic conformal theories).

Publications in connection with the EMOTIONS ARC research project

Carletti, T., Giambagli, L., Bianconi, G., Global Topological Synchronization on Simplicial and Cell Complexes, Physical Rev. Letters, (2023), 130, 187401. DOI: https://doi.org/10.1103/PhysRevLett.130.18740

J-F de Kemmeter, A. Byrne, A. Dunne, T. Carletti and M. Asllani, Emergence of power-law distributions in self-segregation reaction-diffusion processes, Phys. Rev. E, 110, (2024), pp. L012201. DOI: https://doi.org/10.1103/PhysRevE.110.L012201

Asllani, T. Carletti, F. Di Patti, D. Fanelli and F. Piazza, Hopping in the crowd to unveil network topology, Phys. Rev. Letters, 120, (2018), pp. 158301. DOI: https://doi.org/10.1103/PhysRevLett.120.158301

C. Hagendorf, and H. Rosengren, Nearest-neighbour correlation functions for the supersymmetric XYZ chain and Painlevé VI. Commun. Math. Phys. 405, 97 (2024). https://doi.org/10.1007/s00220-024-04977-w

J.-F. de Kemmeter, N. Robert and P. Ruelle, On λ-determinants and tiling problems, Journal of Physics A: Mathematical and Theoretical - Vol. 57, no. 1, p. 015209 (2024) https://doi.org/10.1088/1751-8121/ad0fb2

Ruelle, P., Double tangent method for two-periodic Aztec diamonds, Journal of Statistical Mechanics: Theory and Experiment- Vol. , no.12, p. 123103 (2022) https://doi.org/10.1088/1742-5468/aca4c4

Debin, J.-F. de Kemmeter and P. Ruelle, Fluctuations and arctic curve in the Aztec diamond, Belgian Journal of Physics- Vol. 1, no. 5, p. 18--26 (2022) http://hdl.handle.net/2078.1/275544

The involved partners

 

 

 

    

EMOTIONS | A collaborative Research Action Project (ARC) - October 2024 - September 2029

Funded by the Federation Wallonie-Bruxelles (FWB), ARC projects are Concerted Research Action projects that aim at developing university or inter-university centres of excellence in fundamental research axes and, where possible, that carry out basic and applied research in an integrated manner and aim to make economic and social use of research results. They are awarded based on academic excellence of the applicants, the added value of each research group to achieve goals of research project,  complementary skills of research teams and the methodology of  proposed research program. They typically last for 4 to 5 years. In case of inter-university project, each team is financely supported by its own institution.

More information on the FWB website